Abstract

Recent best management practices established for reducing urban flooding include rain gardens. However, despite their increasing use, rain gardens often lack standardized, data-driven design specifications, particularly concerning infiltration behaviour. In order to forecast the infiltration features of the rain garden, the current work uses conventional and machine learning approaches. In order to conduct research on perennial flower species, a series of small rain gardens were constructed within the hydraulics laboratory at NIT Kurukshetra in Haryana, India. The study involved the utilization of three conventional models (the Philips model, Multi-linear Regression, and the Kostiakov model), as well as two soft computing approaches (M5P tree and Gaussian Process (GP)) to predict the infiltration rate of the rain gardens. The M5P tree model exhibited superior performance compared to other models in the study. The Correlation Coefficient (CC), root mean square error (RMSE), and Nash-Sutcliffe efficiency (NSE) values for the training data set are 0.960, 0.526 cm/hr, and 0.858, respectively, and for validation, data set values are obtained as CC = 0.941, RMSE = 0.667 cm/hr, and NSE = 0.87. The results of this study will be helpful for accurately calculating the infiltration rate of rain gardens.

1 Introduction

1.1 Background

Urbanization has led many landscapes to be changed from pervious surfaces to impervious surfaces, which has increased the amount of runoff to the waterways. During rainfall events, the urban area has a high volume of water, which causes threats such as flooding, erosion, sewer overflow, property damage, etc. India is rapidly urbanizing, and by 2031, the country's urban population may approach 600 million. According to the study from Indian Urban Infrastructure and Services, this demographic transformation would lead to urban and suburban growth (Sivaramakrishnan 2015). For planners, decision-makers, and the administration, urbanization presents a variety of concerns, with urban flooding emerging as one of the most significant issues (Singh and Singh 2011). Urban flooding is mostly caused by inadequate natural drainage, obstruction, extreme weather events, and the expansion of river flood plains (Kumar and Singh 2021; 2023a; 2024a; 2024b; Rafiq et al. 2016). The relationship between runoff and infiltration is illustrated in Figure 1, which shows the changes that occur when the impervious surface area increases.

Figure 1 Effect of imperviousness on runoff and infiltration (Arnold and Gibbons 1996).

Low-impact development (LID) techniques are sustainable land planning and engineering practices that aim to manage stormwater runoff as close to its source as possible. These methods include practices such as green roofs, rain gardens, permeable pavements, and vegetated swales. LID techniques mimic natural processes to infiltrate, evapotranspiration, and reuse stormwater, reducing the impact on the environment and enhancing the resilience of urban areas to flooding and pollution. Among the various low-impact development (LID) techniques, techniques such as rainwater harvesting, storing water in the pond, which slowly infiltrates, etc., are known as Best Management Practices (BMP). Recharging the groundwater is one of the best options for saving rainwater. The rainwater can be diverted towards the groundwater table using LID techniques. Rain gardens are one of the best options, which can enhance the quality of the nearby areas and help the thriving ecosystem (Fletcher et al. 2015). Natural infiltration is an approach that several industries have adopted, and BMP is one of them (Aaron et al. 2012; Davis 2008). The growing media of the rain garden also acts as a filter that removes the dust, pollutants, and harmful ions from the runoff into a rain garden, thus ensuring that good quality water is diverted towards the groundwater table (Osheen and Singh 2020). Vegetation types can also be planted in the rain garden depending on the ion or impurity one wants to remove (Li and Davis 2008; Muerdter et al. 2016; 2018). In terms of hydrologic impact, rain gardens were shown to be more effective than other methods at reducing runoff volume and peak flows (Bhandari et al. 2018; Kumar and Singh 2023b; Osheen and Singh 2019; Yuan et al. 2017).

These approaches (green roofs, rain gardens, permeable pavements, and vegetated swales), which are globally-sensitive approaches to development, serve mainly to protect a hydrologically worthwhile environment after development (Penniman et al. 2013). The primary benefit of LIDs is that they use natural processes instead of specialized labor or additional equipment to remove pollutants from water (Chang 2015). Developing nations can simply apply them because they are affordable compared to other methods. Various factors, including soil permeability, field capacity, organic matter content, and the selection of plant species, influence a rain garden's performance. Rain gardens, also known as bio-retention areas, can be utilized in a wide range of environments to leverage their vegetation (Weerasundara et al. 2016). However, the capacity of infiltration of water in any rain garden is mainly influenced by the soil media and meteorological statistics. It can be easily predicted by the machine learning models, which are cost-effective and demanding.

Recent research and design guidance on rain gardens and bioretention systems indicate that infiltration performance is strongly influenced by soil texture, permeability, vegetation characteristics, and applied hydraulic loading conditions (Davis 2008; Osheen and Singh 2019; Weerasundara et al. 2016). Design-oriented studies commonly recommend sandy loam or engineered soil media with sufficient permeability to ensure effective drainage and to avoid prolonged surface ponding, which may compromise system performance (Kumar and Singh 2023a; Muerdter et al. 2016; 2018). In experimental and pilot-scale investigations, infiltration behaviour is often examined under controlled inflow conditions rather than direct rainfall simulation, as this approach enables clearer evaluation of soil–water–plant interactions without the uncertainty associated with variable rainfall intensity and catchment response (Kumar and Singh 2021; Penniman et al. 2013). Such controlled studies are particularly valuable for developing and validating infiltration prediction models that can support rain garden sizing and performance assessment during the design stage.

Although significant progress has been made in understanding the hydrological performance of rain gardens and bioretention systems, several research gaps remain. Many recent studies focus on long-term field performance and runoff reduction benefits under site-specific conditions, where rainfall variability, catchment complexity, and maintenance effects can obscure the underlying infiltration processes (Kumar and Singh 2023b; Osheen and Singh 2020). While such field-based assessments are essential for evaluating the overall system effectiveness, they often provide limited insight into the isolated influence of soil properties, vegetation characteristics, and hydraulic loading on infiltration behaviour.

Moreover, conventional infiltration models continue to be widely applied in rain garden design, yet their performance relative to modern machine learning approaches has not been systematically evaluated using controlled experimental datasets representative of rain garden conditions (Kumar and Singh 2025a; Mehta et al. 2024). Recent high-impact studies and handbooks emphasize the need for data-driven tools that can improve infiltration forecasting while remaining interpretable and applicable at the design stage (Kumar and Singh 2021; Weerasundara et al. 2016). In this context, the present study contributes by combining a controlled laboratory-based rain garden experiment with a comparative evaluation of traditional infiltration equations and advanced machine learning models, thereby addressing a key gap between empirical design practices and emerging predictive techniques. Accordingly, this study is positioned within recent advances in rain garden research and urban flood mitigation, with a specific focus on improving infiltration prediction through controlled experimentation and comparative modeling.

Machine learning models are used to solve the complex problems of water resources and environmental engineering in the current context. Several researchers have also applied machine learning models for predicting soil infiltration rates (Aradhana et al. 2021; Arora et al. 2024; Kumar et al. 2025; Kumar and Singh 2024c; Kumar and Singh 2025b; Mehta et al. 2024; Nivesh et al. 2022; Puri et al. 2025; Sepahvand et al. 2021; Sihag et al. 2018; 2020; 2021; 2022; Singh et al. 2021a; Singh et al. 2017; 2024; Singh and Minocha 2024a; 2024b; 2025). However, they used the infiltration rate calculated using the double-ring and mini disc infiltrometer.

In this study, the infiltration rate of the soil was calculated using an artificial model of the rain garden, which represents a novel approach. So, the current study aims to investigate the effect of plants on a rain garden. Additionally, conventional models are used to assess the rain garden infiltration rate because it is not always possible to conduct experimental studies. At that time, these techniques may be employed successfully.

To forecast the soil infiltration rate under various plant types and plant densities, this study will compare two soft computing techniques, M5P tree and Gaussian Process (GP), and conventional models, including Philips, Kostikova, and MLR models. The above-mentioned models have never been used to forecast the soil infiltration rate of rain gardens.

2 Materials and Methods

2.1 Experimental setup

Four test rain gardens were built in the hydraulics laboratory at the Civil Engineering Department, NIT Kurukshetra. RG1 and RG2 were the largest, measuring 2m × 2m × 0.1m, and had a denser planting arrangement. The other two rain gardens, RG3 and RG4, were smaller, measuring 1m × 1m × 0.05m. For lateral infiltration prevention and to keep the side face of the soil in place, these rain gardens' sides were encased with acrylic sheets. In this study, four types of plants: scutch grass, candytuft flowers, marigold flowers, and daisy flowers. Information about the plants, including their names and sizes, is included in Table 1. To calculate the infiltration rate of RG1 and RG2, an equal amount of water (100 litres) was applied in rain gardens through a cylindrical storage tank with a capacity of 170 litres (through PVC pipes). Time to infiltration of a given volume of water is noted.

Table 1 Rain garden (RG) name and the number of plants planted.

Plant name	RG1 (No. of plants)	RG2 (No. of plants)	RG3 (No. of plants)	RG4 (No. of plants)	RGs name
Scutch grass	300	240	145	140	RG1, RG2, RG3, RG4
Candytuft flower	220	110	0	0	RG1, RG2
Daisy flower	24	12	12	12	RG1, RG2, RG3, RG4
Marigold flower	0	0	9	9	RG3, RG4

The dimensions and configuration of the experimental rain gardens were selected to represent laboratory-scale systems commonly adopted in rain garden and bioretention research (Li and Davis 2008; Osheen and Singh 2020). A controlled inflow method was employed to focus specifically on infiltration behaviour and to minimize the influence of rainfall variability, which can obscure the role of soil and vegetation in experimental analysis (Kumar and Singh 2021; 2023a). Acrylic sheets were installed along the sidewalls to prevent lateral seepage and to maintain the structural integrity of the soil profile, ensuring that infiltration occurred predominantly in the vertical direction. Similar arrangements have been widely used in experimental studies to obtain repeatable and reliable infiltration measurements (Kumar and Singh 2023b; Muerdter et al. 2018). The selected inflow volumes and application rates were sufficient to generate measurable ponding and infiltration responses within ranges reported for rain garden performance evaluation.

2.2 Materials

Soil samples from different depths, near four corners, and at about the center of the rain gardens were taken for particle size analysis and Atterberg limits tests. The composition of the garden soil in rain gardens consists of sand (75–425µ) and clay (≤ 2µ), accounting for 55.41% and 44.59%, respectively. Consequently, the soil in rain gardens can be classified as sandy loam with a brown color. Laboratory analysis revealed the following Atterberg limits: liquid limit (24.50%), plastic limit (16.00%), and plasticity index (8.50%). The values for the following parameters are listed in Table 2: pH, electrical conductivity (EC), organic content (OC), permeability (K), specific gravity (SG), bulk density (BD), texture, colour, and Atterberg limits.

Table 2 Soil properties of rain gardens.

Soil parameters		Values
pH		7.8
EC (μS/cm)		0.96
OC (%)		0.67
K (m/s)		2.11
SG		2.38
Bulk density (g/cm3)		1.74
Texture	Sand (75–425µ) (%)	55.41
	Clay (≤2µ) (%)	44.59
Color		Brown
Liquid limit (%)		8.50
Plasticity limit (%)		24.50
Plasticity index (%)		16

The time taken for infiltration from start to finish was recorded. Infiltration rate measurements were taken for different plant heights, and overflow from the outlet pipe was collected in a container. Soil infiltration rates were also investigated in relation to plant height, density, and plant type. The spacing and quantity of plants employed in the rain garden were the same throughout the whole experiment. Following that, the inflow rate to the rain garden is 5.7 L/min, with the average inflow rate being 7 L/min.

2.3 Data set

The experiment with the rain garden was done to determine the rate of soil infiltration. Air temperature (t), plant count (n), time (T), inflow to rain garden (r), plant height (H), and soil water content (wc), were the input parameters, and infiltration rate was the output.

3 Modeling Techniques

3.1 Conventional modeling techniques

Kostiakov model (KM)

Equation 1 provides the following information about the Kostiakov model (Subramanya 2020):

(1)

Where:

f(t)	=	infiltration rate,
t	=	time elapsed in the drop of water depth (h), and
a and b	=	constants.

Table 3 gives the values of a and b used in the current investigation.

Table 3 Value of a and b in the Kostiakov model.

Plant name	a	b
Scutch grass	5.27	-0.21
Daisy flower	5.01	0.09
Marigold flower	4.27	0.64
Candytuft flower	3.56	-1.01
Bare soil	5.03	0.18

Philips model (PM)

The Philip’s two-term model relates f(t) (infiltration rate) to t (time), using Equation 2:

(2)

In the Philip's two-term infiltration model, S is the sorptivity (cm/hr^-0.5), which represents the capillary-driven infiltration during the initial stage, whereas K is the saturated hydraulic conductivity (cm/hr), which governs infiltration under gravity-dominated conditions at later times.

Where:

S

=

function of the soil suction potential (Vand et al. 2018).

The values of S and K in the present study can be found in Table 4.

Table 4 Values of S and K in the Philip's model.

Plant name	S	K
Scutch grass	5.71	1.01
Daisy flower	4.51	1.41
Candytuft flower	2.72	1.67
Marigold flower	5.14	1.09
Bare soil	5.43	1.67

Multi-linear regression (MLR)

The MLR approach is utilized to establish the relationship between dependent and independent variables. Equation 3 illustrates the frequently employed formula for MLR (Singh et al. 2021b):

(3)

The dependent variable, which represents the output or infiltration rate, is denoted as f(t) in Equation 3. The regression coefficients, c₀, c₁, c₂, c₃, …, c_n, represent the coefficients of the independent variables, x₁, x₂, x₃, …, x_n.

3.2 Soft computing approaches

M5P tree (M5P)

The M5P tree is a binary decision tree that predicts continuous numerical quantities using a linear regression function at the leaf (terminal node). For the development of the model tree, this approach uses two steps. Splitting the criteria in the first stage creates a decision tree. This method of splitting criteria depends on how the class value's standard deviation is handled. Splitting is deemed to be pure when there is less standard deviation in the child node than in the parent node (Quinlan 2006). The M5P tree selects the split that minimizes the errors of all feasible splits. The splitting of the data might lead the tree to become too large and result in overfitting. The next step is to use the pruning procedure to remove overfitting. Replacing the subtrees with a linear regression function prunes the overgrown tree. This tree-generation method divides parameter space into surfaces and creates a linear regression model in each of them. The M5P tree method measures the error value and uses the squared standard deviation of the values reaching the last nodes to estimate the expected error reduction (Singh et al. 2019). Standard reduction is given in Equation 4 as:

(4)

Where:

SDR	=	standard deviation reduction,
N	=	group of samples that reach the node,
Ni	=	result of a subset of the prospective set's examples, and
sd	=	standard deviation.

Gaussian Process (GP)

GP regression relies upon the postulation that nearby observation must mutually share information, and it is an approach for mentioning earlier straight over the function space. The simplification of Gaussian distribution is known as Gaussian regression. The matrix and vector of Gaussian distribution are expressed as covariance and mean in GP regression. Due to having earlier knowledge of function reliance and data, the validation for generalization is not essential. GP regression models can recognize the foreseen distribution consequent to the input test data (Williams 2007). A GP is the collection of numbers of random variables, and any finite number of them has a collective multivariate Gaussian distribution. Assuming that u and v represent the input and output domains, respectively, the training dataset consists of n input–output pairs (g_i, h_i), which are assumed to be independently and identically distributed.

In the regression case, it is commonly assumed that the set h belongs to the real numbers (h ⊆ Re). Consequently, a Gaussian Process (GP) on p can be defined using the mean function v0, which maps elements from the real numbers to u, and the covariance function µ, which operates on pairs of elements from u and maps them to the real numbers (µ: u × u Re). To obtain a comprehensive understanding of GP, it is recommended that readers refer to the detailed explanations provided by Kuss (2006).

4 Model Performance

Using statistical measures including CC, RMSE, and NSE, the effectiveness of conventional and soft computing models was studied. The relationships used in the study are given below:

CC: calculated using Equation 5:

(5)

RMSE: calculated using Equation 6:

(6)

NSE is calculated using Equation 7:

(7)

Where:

CC	=	correlation coefficient,
RMSE	=	root mean square error,
NSE	=	Nash-Sutcliffe efficiency,
m	=	number of observations,
ci	=	observed infiltration rate,
ei	=	predicated infiltration rate, and
	=	average observed infiltration rate.

4.1 Data set

A total of 166 observations were used in modeling for this study. For the training data set, 75% of the data were used, and for validation, the remaining 25% were used.

4.2 Detail of kernel functions

Kernel feature design strategies are included in GP-based regression methods. GP has a lot of nuclear operations. This work used the GP method for two kernels: the GP PUK kernel and the GP RBF kernel.

The radial basis kernel (RBF) is calculated using Equation 8:

(8)

 The Pearson VII kernel function (PUK) is calculated using Equation 9:

(9)

Where:

γ, σ, and ω	=	kernel parameters,
a and b	=	input vectors, and
||a-b||	=	Euclidean distance between a and b.

It is well known that the estimation efficiency of GP "a–b" depends on appropriate adjustments of the meta-parameters, Gaussian noise parameters, C, γ, σ, and ω. The choice of Gaussian noise, C, γ, σ, and ω determines the complexity of the predictive (regression) model. This study selected key parameters (i.e., C, γ, σ, ω and Gaussian noise) using physical techniques. Appropriate values of various key parameters are chosen to minimize RMSE and maximize CC. The same kernel parameters were used for GP regression. Table 5. shows all optimal values of the soft computing techniques used in this study with WEKA software (Eibe et al. 2016).

Table 5 Primary parameters using GP and M5P tree.

Approaches	Primary parameters
M5P	m = 5.0
GP RBF	Gaussian noise = 0.80, γ = 3.50
GP PUK	Gaussian noise = 0.80, ω = 0.02, σ = 0.50
GP RBF	C = 2.0, γ = 3.50
GP PUK	C = 2.0, ω = 0.02, σ = 0.50

5 Results and Discussion

The findings from predicting the soil infiltration rate were acquired using the suggested conventional models and soft computing techniques discussed above. The infiltration rate was predicted by comparing the three conventional models and the two soft computing techniques.

5.1 Performance of conventional models

The scatter plots in Figures 2 and 3 depict the fit line at a 45° angle with respect to the x-axis, indicating a perfect agreement between the predicted and observed values generated by the model. However, it is evident from the other straight lines in the graphs that the model occasionally overestimated or underestimated the values, as indicated by the error lines of ±25%.

Figure 2 (a) Correlation between observed and projected infiltration rates for both the training and testing datasets of KM; (b) Correlation between observed and projected infiltration rates for both the training and testing datasets of PM; and (c) Correlation between observed and projected infiltration rates for both the training and testing datasets MLR.

Figure 2(b) specifically highlights the superior performance of the PM model compared to the other two models (Figure 2a and 2c). This is evident from the predicted infiltration rate maximum values, which closely align with the agreement line and fall within the ±25% error range. The PM model exhibits favourable values for CC (0.583), RMSE (2.235), and NSE (0.339) for the training dataset, and similarly for the validation dataset (0.630, 2.320, and 0.396). These metrics, as presented in Table 6, play a crucial role in determining the suitability of a technique or model based on its performance. In this context, KM outperforms MLR in the other two models.

5.2 Performance of soft computing approaches

Figure 3(a) gives the performance of M5P, Figures 3(b) and 3(c) display the performance of the Gaussian Process with PUK and RBF kernels. The comparison shows that the M5P model outperforms the Gaussian Process model, as evidenced by the predicted infiltration rate maximum values closely aligning with the agreement line and falling within the ±25% error range. The M5P Tree model demonstrates favourable values for CC (0.960), RMSE (0.526), and NSE (0.858) for the training dataset and similarly for the validation dataset (0.941, 0.667, and 0.870).

Figure 3 (a) Correlation between observed and projected infiltration rates for both the training and testing datasets of M5P; (b) Correlation between observed and projected infiltration rates for both the training and testing datasets of GP PUK Kernel; and (c) Correlation between observed and projected infiltration rates for both the training and testing datasets of GP RBF Kernel.

Figure 4 is a residual error box plot for different soft computing techniques. For measuring the infiltration rate of rain gardens, Kumar and Sihag (2019), Yetilmezsoy et al. (2021), and Sihag et al. (2024) have utilized data-driven models for prediction. In this study, the best-performing model (M5P Tree) is compared with the models from these previous studies, as summarized in Table 6. The performance of the models, based on the seven input and one output parameter, is summarized in Table 7. Interestingly, the Gaussian Process model demonstrates superior performance compared to the other models utilized in this study.

Figure 4 Residual errors for soft computing techniques.

Table 6 Comparison of this study’s results with previously published results based on statistical parameters.

Literature studies	Model	Statistical parameters
		CC	RMSE
This study	M5P	0.96	0.53
(Kumar and Sihag 2019)	ANFIS_triangular	0.790	17.316
(Kumar and Sihag 2019)	Random forest	0.867	13.504
(Yetilmezsoy et al. 2021).	GPR-PUKF	0.8939	0.2110
(Sihag et al. 2024)	M5P	0.9543	5.8006

Table 7 Comparison of different modeling techniques on a testing dataset.

Model name/Technique	Training data set			Testing data set
	CC.	RMSE	NSE	CC.	RMSE	N.S.E.
Philips model	0.58	2.24	0.34	0.63	2.32	0.40
Kostiakov model	0.50	4.91	0.45	0.58	2.31	0.40
MLR	0.55	2.35	0.31	0.51	2.93	0.24
M5P	0.96	0.53	0.86	0.94	0.67	0.87
GP PUK Kernel	0.92	0.85	0.77	0.88	1.02	0.70
GP RBF Kernel	0.59	1.64	0.12	0.58	1.88	-0.02

The M5P model's exceptional success is due to its ability to manage intricate, nonlinear interactions among variables by partitioning the dataset into smaller, homogenous subsets and using linear regression at each leaf node. The infiltration dataset in this work includes several interacting environmental and design elements, such as air temperature, inflow rate, plant height, and soil water content, which often exhibit nonlinear behaviour and threshold effects. The model's capacity to segment the data and represent localised behaviours makes it particularly adept at capturing these interactions. Moreover, its pruning mechanism mitigates overfitting and improves generalisation performance, making it particularly appropriate for the infiltration features seen in rain gardens.

6 Conclusion

This study investigates the soil infiltration rate of various types of plants planted within a rain garden. Through field observations, it was found that scutch grass exhibits the highest infiltration rate, while the daisy flower plant exhibits the lowest infiltration rate. The descending order of infiltration rates is as follows: scutch grass plants, candytuft flower plants, marigold flower plants, and daisy flower plants.

Three conventional models and two soft computing techniques were employed to predict the soil infiltration rate. The results indicate that soft computing techniques provide more accurate predictions than conventional methods. Among the models utilized, the M5P tree model was the most suitable. According to the performance metrics presented in Table 6, the M5P tree model demonstrated significantly higher performance for both the training dataset (CC = 0.960, RMSE = 0.526, and NSE = 0.858) and the testing dataset (CC = 0.941, RMSE = 0.667, and NSE = 0.87) when compared to other models such as GP, Philip's model, Kostiakov model, and MLR.

The findings of this study can guide the selection of plant species in rain garden designs to optimize soil infiltration rates, improve water management, and reduce runoff. Future research could focus on validating these results across different climates and soil types. Additionally, the application of soft computing techniques, particularly the M5P tree model, may be expanded to predict infiltration rates in various other environmental contexts.

Recent SuDS (Sustainable Urban Drainage Systems) planning frameworks and the increasing use of sensor-based monitoring systems emphasize the importance of performance verification in rain garden design; however, a detailed examination of these aspects lies beyond the scope of the present laboratory-based investigation.

Acknowledgment

The first author (Sandeep Kumar) thanks MHRD, GOI, for financially supporting the present work through a Ph.D. scholarship grant (2K19/NITK/Ph.D./61900082).

Funding

The National Institute of Technology (NIT) Kurukshetra Director and the Ministry of Education (MOE), Government of India, together provide financial support for the present research project in the form of a PhD scholarship award with reference number 2K19/NITK/PHD/61900082.

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20. Kuss, M. 2006. “Gaussian Process Models for Robust Regression , Classification , and Reinforcement Learning.” Doctoral dissertation, Technische Universität Darmstadt, Darmstadt, Germany. https://doi.org/10.26083/tuprints-00000674
21. Li, H. and A.P. Davis. 2008. “Urban Particle Capture in Bioretention Media. II: Theory and Model Development.” Journal of Environmental Engineering 134 (6): 419–432. https://doi.org/10.1061/(ASCE)0733-9372(2008)134:6(419)
22. Mehta, V., S. Hasanvand, A. Sepahvand, P. Sihag, N. Beiranvand, and B. Singh. 2024. “A benchmark comparison of AI-based modeling of soil in fi ltration rates.” Journal of Hydroinformatics 26 (12): 3060–3079. https://doi.org/10.2166/hydro.2024.086
23. Muerdter, C., E. Özkök, L. Li, and A.P. Davis. 2016. “Vegetation and Media Characteristics of an Effective Bioretention Cell.” Journal of Sustainable Water in the Built Environment 2 (1): 04015008. https://doi.org/10.1061/JSWBAY.0000804
24. Muerdter, C.P., C.K. Wong, and G.H. Lefevre. 2018. “Emerging investigator series: The role of vegetation in bioretention for stormwater treatment in the built environment: Pollutant removal, hydrologic function, and ancillary benefits.” Environmental Science: Water Research and Technology 4 (5): 592–612. https://doi.org/10.1039/C7EW00511C
25. Nivesh, S., D. Negi, P.S. Kashyap, S. Aggarwal, B. Singh, B. Saran, et al. 2022. “Prediction of river discharge of Kesinga sub‑catchment of Mahanadi basin using machine learning approaches.” Arabian Journal of Geosciences 15, 1369. https://doi.org/10.1007/s12517-022-10555-y
26. Osheen and K.K. Singh. 2019. “Rain Garden—A Solution to Urban Flooding: A Review.” In: Agnihotri, A., Reddy, K., Bansal, A. (eds), Sustainable Engineering. Lecture Notes in Civil Engineering, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-13-6717-5_4
27. Osheen and K.K. Singh. 2020. “The Influence of Slope Profile on Rain Gardens’ Hydrological Performance.” World Environmental and Water Resources Congress 2020 Proceedings, 145–153. https://doi.org/10.1061/9780784482988.015
28. Penniman, D., M. Hostetler, T. Borisova, and G. Acomb. 2013. “Capital Cost Comparisons between Low Impact Development (LID) and Conventional Stormwater Management Systems in Florida.” Suburban Sustainability 1, 2. https://doi.org/10.5038/2164-0866.1.2.1
29. Puri, D., P. Sihag, M.S. Thakur, and B. Singh. 2025. “Aeration of square jets in an open channel: Experimental analysis and modeling.” AQUA – Water Infrastructure, Ecosystems and Society 74 (1): 68–91. https://doi.org/10.2166/aqua.2024.247
30. Quinlan, J.R. 2006. “Learning With Continuous Classes 2. Constructing Model Trees.” In: 5^th Australian Join Conference on Artificial Intelligence 92, 343–348.
31. Rafiq, S., R. Salim, and I. Nielsen. 2016. “Urbanization, openness, emissions, and energy intensity: A study of increasingly urbanized emerging economies.” Energy Economics 56, 20–28. https://doi.org/10.1016/j.eneco.2016.02.007
32. Sepahvand, A., B. Singh, M. Ghobadi, and P. Sihag. 2021. “Estimation of infiltration rate using data-driven models.” Arabian Journal of Geosciences 14, 42. https://doi.org/10.1007/s12517-020-06245-2
33. Sihag, P., M. Kumar, and B. Singh. 2021. “Assessment of infiltration models developed using soft computing techniques.” Geology, Ecology, and Landscapes 5 (4): 241–251. https://doi.org/10.1080/24749508.2020.1720475
34. Sihag, P., T. Mehta, S. Sh, and C. Baliram. 2024. “Predictive modelling of nitrogen dioxide using soft computing techniques in the Agra, Uttar Pradesh , India.” Physics and Chemistry of the Earth 134, 103589. https://doi.org/10.1016/j.pce.2024.103589
35. Sihag, P., B. Singh, A. Bin, and H. Azamathulla. 2022. “Prediction of manning ’ s coef fi cient of roughness for high-gradient streams using M5P.” Water Supply 22 (3): 2707–2720. https://doi.org/10.2166/ws.2021.440
36. Sihag, P., B. Singh, S. Gautam, and S. Debnath. 2018. “Evaluation of the impact of fly ash on infiltration characteristics using different soft computing techniques.” Applied Water Science 8, 187. https://doi.org/10.1007/s13201-018-0835-2
37. Sihag, P., B. Singh, A. Sepah Vand, and V. Mehdipour. 2020. “Modeling the infiltration process with soft computing techniques.” ISH Journal of Hydraulic Engineering 26 (2): 138–152. https://doi.org/10.1080/09715010.2018.1464408
38. Singh, A., B. Singh, and P. Sihag. 2021a. “Experimental Investigation and Modeling of Aeration Efficiency at Labyrinth Weirs.” Soft Computing in Civil Engineering 5 (3, 17): 15–31. https://doi.org/10.22115/SCCE.2021.284637.1311
39. Singh, B. and V.K. Minocha. 2024a. “Approximation in scour depth around spur dikes using novel hybrid ensemble data-driven model.” Water Science & Technology 89 (4): 962–975. https://doi.org/10.2166/wst.2024.025
40. Singh, B. and V.K. Minocha. 2024b. “Clear Water Scour Depth Prediction using Gradient Boosting Machine and Deep Learning.” IOP Conference Series: Earth and Environmental Science 1327, 012030. https://doi.org/10.1088/1755-1315/1327/1/012030
41. Singh, B. and V.K. Minocha. 2025. “Hybrid ensemble models for scour depth prediction around spur dikes.” Measurement 256 (B): 118277. https://doi.org/10.1016/j.measurement.2025.118277
42. Singh, B., A. Sepahvand, P. Sihag, K. Singh, C. Prabha, A. Nag, et al. 2024. “Development of soft computing- based models for forecasting water quality index of Lorestan Province, Iran.” Scientific Reports 14 (1): 1–18. https://doi.org/10.1038/s41598-024-76894-w
43. Singh, B., P. Sihag, and S. Deswal. 2019. “Modelling of the impact of water quality on the infiltration rate of the soil.” Applied Water Science 9, 15. https://doi.org/10.1007/s13201-019-0892-1
44. Singh, B., P. Sihag, A. Parsaie, and A. Angelaki. 2021b. “Comparative analysis of artificial intelligence techniques for the prediction of infiltration process.” Geology, Ecology, and Landscapes 5 (2): 109–118. https://doi.org/10.1080/24749508.2020.1833641
45. Singh, B., P. Sihag, and K. Singh. 2017. “Modelling of impact of water quality on infiltration rate of soil by random forest regression.” Modeling Earth Systems and Environment 3, 999–1004. https://doi.org/10.1007/s40808-017-0347-3
46. Singh, B. and T. Singh. 2022. “Soft Computing-based prediction of compressive strength of high strength concrete.” In Applications of Computational Intelligence in Concrete Technology. CRC Press. pp. 207-218. https://doi.org/10.1201/9781003184331
47. Singh, R.B. and S. Singh. 2011. “Rapid urbanization and induced flood risk in Noida, India.” Asain Geographer 28 (2): 147–169. https://doi.org/10.1080/10225706.2011.629417
48. Sivaramakrishnan, K.C. 2015. “Infrastructure and Services.” Governance of Megacities: Fractured Thinging, Fragmented Setup. Available online: Oxford Academic, Delhi, pp. 56–81. https://doi.org/10.1093/acprof:oso/9780199454136.003.0004
49. Subramanya, K. 2020. Engineering Hydrology, Fifth edition. McGraw-Hill, New Delhi, India.
50. Vand, A.S., P. Sihag, B. Singh, and M. Zand. 2018. “Comparative Evaluation of Infiltration Models.” KSCE Journal of Civil Engineering 22 (10): 4173–4184. https://doi.org/10.1007/s12205-018-1347-1
51. Weerasundara, L., C.N. Nupearachchi, P. Kumarathilaka, B. Seshadri, N. Bolan, and M. Vithanage. 2016. “Bio-retention Systems for Storm Water Treatment and Management in Urban Systems.”  In: Ansari, A., Gill, S., Gill, R., Lanza, G., Newman, L. (eds), Phytoremediation. Springer, Cham.175–200. https://doi.org/10.1007/978-3-319-41811-7_10
52. Williams, C. 2007. “Gaussian Processes for Machine Learning (Presentation).” Institute for Adaptive and Neural Computation.
53. Yetilmezsoy, K., P. Sihag, E. Kıyan, and B. Doran. 2021. “A benchmark comparison and optimization of Gaussian process regression , support vector machines , and M5P tree model in approximation of the lateral confinement coefficient for CFRP-wrapped rectangular/square RC columns.” Engineering Structures 246, 113106. https://doi.org/10.1016/j.engstruct.2021.113106
54. Yuan, J., N. Dunnett, and V. Stovin. 2017. “The influence of vegetation on rain garden hydrological performance.” Urban Water Journal 14 (10): 1083–1089. https://doi.org/10.1080/1573062X.2017.1363251